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  Volume 3, Issue 5, Article 73
 
A Monotonicity Property of the Gamma Function
    Authors: Hendrik Vogt, Jürgen Voigt,  
    Keywords: Gamma function, Strictly completely monotone.  
    Date Received: 11/01/01  
    Date Accepted: 29/07/02  
    Subject Codes:

33B15

  
    Editors: Andrea Laforgia,  
 
    Abstract:

It is shown that the function $x mapsto 1+frac1xlnGamma(x+1)-ln(x+1)$ is strictly completely monotone on $(-1,infty)$ and tends to one as $xto-1$, to zero as $xtoinfty$. This property is derived from a suitable integral representation of $lnGamma(x+1)$.

         
       
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